Finite Group Databasebeta

← #14816717

Subgroups — #14816717

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×#10622485C211yesmaximal, characteristic
3#13072462C211yesmaximal, characteristic, complemented
4#13071517C211yesmaximal, characteristic, complemented
5#13070141C211yesmaximal, characteristic, complemented
6#13070090C211yesmaximal, characteristic, complemented
7#13070001C211yesmaximal, characteristic, complemented
8#13069348C211yesmaximal, characteristic, complemented
9#13069176C211yesmaximal, characteristic, complemented
10#13068965C211yesmaximal, characteristic
11#13068963C211yesmaximal, characteristic
12#13068864C211yesmaximal, characteristic, complemented
13#13068864C211yesmaximal, characteristic, complemented
14#13068860C211yesmaximal, characteristic, complemented
15C11×#2057C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999—21no—
18C22×D88C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4⋊C4×D11—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C11×#389C2211yescharacteristic
27#10622844—21no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622700—24no—
32#10622607—21no—
33#10622602—21no—
34#10622602—21no—
35#10622601C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622485—24no—
51#10622281—21no—
52#10622280—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D44C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79#66999—44no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4D411yescharacteristic
96C2×Dic11⋊C4D411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×D88—22no—
102C2×D88—22no—
103C2×D88Q814yescomplemented
104#66946—22no—
105#66946—22no—
106#66946—22no—
107#66946—22no—
108#66946—41no—
109#66946—41no—
110C4⋊C4×D11—44no—
111C4×D44—22no—
112C4×D44—41no—
113C11×#107—22no—
114C11×#107—41no—
115C11×#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66885—22no—
122#66885—41no—
123C8×Dic11—22no—
124#66873—22no—
125#66873—22no—
126#66873—22no—
127#66873D414yes—
128#66871—22no—
129#66871—22no—
130#66871—22no—
131C4⋊(C11⋊C8)—22no—
132#26368—111nomaximal, Sylow
133C23×D11—21no—
134C23×D11—21no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11—81no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44C2×D412yes—
160C2×D44C2×Q812yes—
161C2×D44C2×Q812yes—
162C2×D44#4112yes—
163C2×C4×D11—24no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
174C2×C4×D11—81no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×Q812yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4C2×D412yes—
190C11×C4⋊C4#4112yes—
191C42×C11—21no—
192C42×C11—21no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—42no—
206C4⋊Dic11—42no—
207Dic11⋊C4—41no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211Dic11⋊C4D814yescomplemented
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8C2×D412yes—
222D88—28no—
223C2×#474—111no—
224C2×C4×D8—111no—
225#2452—111no—
226D4×C4⋊C4—111no—
227#2093—111no—
228#2083—111no—
229#2067—111no—
230#2057D1111yescharacteristic, complemented
231#1942—111no—
232#1916—111no—
233#1879—111no—
234#1879—111no—
235#1862—111no—
236#1862—111no—
237#1862—111no—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253Q8×C11—84no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11C2×D812yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C112−1+411yescharacteristic
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11C2×D812yes—
295C2×Dic11C2×D812yes—
296D44—22no—
297D44—22no—
298D44—22no—
299D44—22no—
300D44—22no—
301D44—41no—
302D44—41no—
303D44C22⋊Q814yescomplemented
304C4×D11—48no—
305C4×D11—84no—
306C4×D11—84no—
307C4×D11—84no—
308C8×C11—22no—
309C8×C11—41no—
310C11⋊C8—22no—
311C11⋊C8—41no—
312C22×D8—111no—
313C2×C4⋊Q8C2×D1111yescharacteristic
314C2×C22⋊Q8—221no—
315C2×C4×D4—111no—
316C2×C4×D4—111no—
317C2×C4×D4—111no—
318C2×C4×D4—111no—
319C22×C4⋊C4—221no—
320#474—224no—
321C4×D8—224no—
322C2×#107—111no—
323C2×#107—111no—
324C2×#107—111no—
325C2×#107C2×D1111yescharacteristic
326C2×#107C2×D1111yescharacteristic
327C2×C4⋊C8—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×C4×C8—111no—
335#396—221no—
336#393—221no—
337#390—111no—
338#390—111no—
339#389—111no—
340#389—111no—
341#389—111no—
342#389C2×D1111yescharacteristic
343#385—221no—
344#385—221no—
345#385—221no—
346#384—111no—
347#380—221no—
348C4×C4⋊C4—111no—
349#340—111no—
350#340—111no—
351#340C2×D1111yescharacteristic
352#340C2×D1111yescharacteristic
353#336—111no—
354#336—111no—
355#336—111no—
356#336C2×D1111yescharacteristic
357C22×C11#52511yescharacteristic
358C22×C11D4211yescharacteristic
359C22×C11D4×Q811yescharacteristic
360C22×C11C22×D811yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57611yescharacteristic
363C22×C11#57811yescharacteristic
364C2×D11—24no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C4×C11—22no—
379C4×C11—42no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11C2×C22⋊Q811yescharacteristic
385C4×C11#53911yescharacteristic
386C4×C11#54711yescharacteristic
387C4×C11#55411yescharacteristic
388Dic11—22no—
389Dic11—22no—
390Dic11—41no—
391Dic11—41no—
392Dic11—81no—
393Dic11—81no—
394C22×Q8—21no—
395C22×D4—111no—
396C22×D4—111no—
397C23×C4—221no—
398C23×C4—221no—
399C23×C4—221no—
400C23×C4—221no—
401C2×D8—114no—
402C2×D8—222no—
403C2×D8—222no—
404C22×C8—111no—
405C22×C8—111no—
406C22×C8C22×D1111yescharacteristic
407C22×C8C22×D1111yescharacteristic
408C4⋊Q8—22no—
409C4⋊Q8—41no—
410C22⋊Q8—444no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4—441no—
417C4×D4—441no—
418C4×D4—441no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—444no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42C22×D1111yescharacteristic
446#107—22no—
447#107—41no—
448#107—222no—
449#107—222no—
450#107—222no—
451C4⋊C8—222no—
452#102—114no—
453#102—222no—
454#102—222no—
455#102—222no—
456#102—222no—
457#102—441no—
458C4×C8—222no—
459#95—21no—
460#95—111no—
461#95—111no—
462#95—221no—
463#95—221no—
464#95—221no—
465C2×C11#244911yescharacteristic
466C2×C11#310011yescharacteristic
467C2×C11#312411yescharacteristic
468C2×C11#326911yescharacteristic
469C2×C11D4×D811yescharacteristic
470C2×C11Q8×D811yescharacteristic
471C2×C11#338911yescharacteristic
472D11—44no—
473D11—82no—
474C24—221no—
475C24—221no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—81no—
479C2×D4—112no—
480C2×D4—112no—
481C2×D4—112no—
482C2×D4—112no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—224no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—881no—
511C22×C4—881no—
512C22×C4—881no—
513C22×C4D4×D1111yescharacteristic
514C22×C4D4×D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516D8—228no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—112no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8Q8×D1112yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—114no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—441no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—881no—
548C4⋊C4D4×D1112yes—
549C4⋊C4#434312yes—
550C22⋊C4—224no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—881no—
558C42—21no—
559C42—21no—
560C42—221no—
561C42—221no—
562C42—221no—
563C42—221no—
564C11#2636811yescharacteristic, complemented, Sylow
565C23—222no—
566C23—222no—
567C23—222no—
568C23—222no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23C2×D4×D1111yescharacteristic
580Q8—84no—
581D4—114no—
582D4—222no—
583D4—222no—
584D4—222no—
585D4—222no—
586D4—222no—
587D4—441no—
588D4—441no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—112no—
607C2×C4—112no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—448no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—884no—
626C2×C4—884no—
627C2×C4—884no—
628C2×C4D8×D1112yes—
629C2×C4C2×D4×D1111yescharacteristic
630C2×C4#6703711yescharacteristic
631C2×C4C2×Q8×D1111yescharacteristic
632C2×C4C2×#434311yescharacteristic
633C2×C4#6704011yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C8—22no—
636C8—41no—
637C8—222no—
638C8—441no—
639C22—224no—
640C22—442no—
641C22—442no—
642C22—442no—
643C22—442no—
644C22—442no—
645C22—442no—
646C22—442no—
647C22—442no—
648C22—442no—
649C22—881no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22#1062312111yescharacteristic
654C22#1062315811yescharacteristic
655C22#1062325811yescharacteristic
656C22C2×D8×D1111yescharacteristic
657C22#1062329711yescharacteristic
658C22#1062330511yescharacteristic
659C22#1062330811yescharacteristic
660C4—22no—
661C4—42no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—222no—
667C4—222no—
668C4—441no—
669C4—441no—
670C4—881no—
671C4—881no—
672C4D11×C22⋊Q811yescharacteristic
673C4#1062316911yescharacteristic
674C4#1062325711yescharacteristic
675C4#1062326111yescharacteristic
676C2—444no—
677C2—882no—
678C2#1307241811yescharacteristic
679C2#1307861811yescharacteristic
680C2#1307888511yescharacteristic
681C2#1308017411yescharacteristic
682C2#1308028611yescharacteristic
683C2#1308146811yescharacteristic
684C2#1308157111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2057C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenter#2057D11
hypocenterC11#26368
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
3. #13072462C2semidirect
4. #13071517C2semidirect
5. #13070141C2semidirect
6. #13070090C2semidirect
7. #13070001C2semidirect
8. #13069348C2semidirect
9. #13069176C2semidirect
12. #13068864C2semidirect
13. #13068864C2semidirect
14. #13068860C2semidirect
15. C11×#2057C2semidirect
103. C2×D88Q8semidirect
211. Dic11⋊C4D8semidirect
230. #2057D11semidirect
303. D44C22⋊Q8semidirect
564. C11#26368semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106227002
C2×#106224852
#130724622
#130715172
#130701412
#130700902
#130700012
#130693482
#130691762
#130689652
#130689632
#130688642
#130688602
C11×#20572
#2636811